Joining seperate objects in armature?
There's a bad rigging of the nose, i.e. bones influencing the nose while they are not supposed to.

So what you need to do is select the whole mesh in Edit mode and remove the nose vertices from all groups, then assign them to the good vertex group which is "spine.006" (name of the head bone).

Now when you rotate the head you can see that the nose goes far away, but this time it's because the head is flattened, this is because the head is also bad rigged. So do the same things, and it will work.